url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | have hP'₁_le : P'₁ ≤ Subalgebra.toSubmodule B := by
simp only [← hs, Finset.coe_union, Submodule.span_le, Subalgebra.coe_toSubmodule, B]
exact subset_trans (Set.subset_union_left _ _) Algebra.subset_adjoin | case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG... | case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | have k : (Subalgebra.inclusion hBA).toLinearMap ∘ₗ P.subtype
= Submodule.inclusion hP'₁_le ∘ₗ Submodule.inclusion hP₁_le ∘ₗ j := by ext; rfl | case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG... | case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | have k' : (Subalgebra.inclusion hBA).toLinearMap ∘ₗ P'.subtype
= Submodule.inclusion hP'₁_le ∘ₗ Submodule.inclusion hP₁_le ∘ₗ j' := by ext; rfl | case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG... | case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | rw [k, k'] | case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG... | case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | simp only [LinearMap.rTensor_comp, LinearMap.comp_apply] | case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG... | case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | rw [← hu₁, ← hu'₁, h] | case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | simp only [Submodule.coeSubtype, Submodule.map_sup, P₁] | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | apply Submodule.mem_sup_left | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | case a
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | use p | case a
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ... | case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTen... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | simp only [SetLike.mem_coe] | case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ... | case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTen... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | exact ⟨hp, rfl⟩ | case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTen... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | simp only [Submodule.coeSubtype, Submodule.map_sup, P₁] | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | apply Submodule.mem_sup_right | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | case a
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | use p | case a
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ... | case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTen... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | simp only [SetLike.mem_coe] | case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ... | case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTen... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | exact ⟨hp, rfl⟩ | case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTen... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | rw [hu₁, hu'₁] | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | simp only [← LinearMap.comp_apply, ← LinearMap.rTensor_comp] | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | have hj₁ : P₁.subtype ∘ₗ j = (Subalgebra.val A).toLinearMap ∘ₗ P.subtype := by ext; rfl | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | have hj'₁ : P₁.subtype ∘ₗ j' = (Subalgebra.val A).toLinearMap ∘ₗ P'.subtype := by ext; rfl | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | rw [hj₁, hj'₁] | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | simp only [LinearMap.rTensor_comp, LinearMap.comp_apply] | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | rw [hu, hu', h] | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | ext | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | rfl | case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTen... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | ext | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R]... | case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | rfl | case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTen... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | simp only [B, ← hw] | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | apply Algebra.adjoin_mono | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R... | case H
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u :... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | simp only [Finset.coe_union, Set.subset_union_right] | case H
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case H
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTe... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | simp only [← hs, Finset.coe_union, Submodule.span_le, Subalgebra.coe_toSubmodule, B] | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | exact subset_trans (Set.subset_union_left _ _) Algebra.subset_adjoin | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | ext | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R... | case h.a
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | rfl | case h.a
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.r... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | ext | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u : ↥P ⊗[R... | case h.a
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq | [233, 1] | [288, 24] | rfl | case h.a
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t'
P : Submodule R ↥A
hP : P.FG
u... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t t' : ↥A ⊗[R] N
h✝ : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.r... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | Subalgebra.FG.sup | [290, 1] | [297, 49] | rw [Algebra.adjoin_union, hs.2, hs'.2] | R✝ : Type u_1
S✝ : Type u_2
N : Type u_3
inst✝⁷ : CommRing R✝
inst✝⁶ : CommRing S✝
inst✝⁵ : Algebra R✝ S✝
inst✝⁴ : AddCommGroup N
inst✝³ : Module R✝ N
R : Type u_4
S : Type u_5
inst✝² : CommSemiring R
inst✝¹ : Semiring S
inst✝ : Algebra R S
A A' : Subalgebra R S
hA : A.FG
hA' : A'.FG
s : Set S
hs : s.Finite ∧ Algebra.a... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
R✝ : Type u_1
S✝ : Type u_2
N : Type u_3
inst✝⁷ : CommRing R✝
inst✝⁶ : CommRing S✝
inst✝⁵ : Algebra R✝ S✝
inst✝⁴ : AddCommGroup N
inst✝³ : Module R✝ N
R : Type u_4
S : Type u_5
inst✝² : CommSemiring R
inst✝¹ : Semiring S
inst✝ : Algebra R S
A A' : Subalgebra ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq' | [299, 1] | [320, 10] | let A'' := A ⊔ A' | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toLinearMa... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toLinearMa... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq' | [299, 1] | [320, 10] | let hA_le := (le_sup_left : A ≤ A'') | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toLinearMa... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toLinearMa... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq' | [299, 1] | [320, 10] | let hA'_le := (le_sup_right : A' ≤ A'') | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toLinearMa... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toLinearMa... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq' | [299, 1] | [320, 10] | have hj : (Subalgebra.val A'').comp (Subalgebra.inclusion hA_le)
= Subalgebra.val A := by ext; rfl | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toLinearMa... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toLinearMa... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq' | [299, 1] | [320, 10] | have hj' : (Subalgebra.val A'').comp (Subalgebra.inclusion hA'_le)
= Subalgebra.val A' := by ext; rfl | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toLinearMa... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toLinearMa... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq' | [299, 1] | [320, 10] | rw [← hj, ← hj'] at h | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toLinearMa... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
A'' : Subalgebra R S := A ⊔ A'
hA_le : A ≤ A ⊔ A' := le_sup_left
hA'_le : A' ≤ A ⊔ A' ... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq' | [299, 1] | [320, 10] | simp only [AlgHom.comp_toLinearMap, LinearMap.rTensor_comp, LinearMap.comp_apply] at h | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
A'' : Subalgebra R S := A ⊔ A'
hA_le : A ≤ A ⊔ A' := le_sup_left
hA'_le : A' ≤ A ⊔ A' ... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
A'' : Subalgebra R S := A ⊔ A'
hA_le : A ≤ A ⊔ A' := le_sup_left
hA'_le : A' ≤ A ⊔ A' ... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
A'' : Subalgebra R S := A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq' | [299, 1] | [320, 10] | let ⟨B, hB_le, hB, h⟩ := TensorProduct.Algebra.eq_of_fg_of_subtype_eq
(Subalgebra.FG.sup hA hA') _ _ h | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
A'' : Subalgebra R S := A ⊔ A'
hA_le : A ≤ A ⊔ A' := le_sup_left
hA'_le : A' ≤ A ⊔ A' ... | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
A'' : Subalgebra R S := A ⊔ A'
hA_le : A ≤ A ⊔ A' := le_sup_left
hA'_le : A' ≤ A ⊔ A' ... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
A'' : Subalgebra R S := A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq' | [299, 1] | [320, 10] | use B, le_trans hA_le hB_le, le_trans hA'_le hB_le, hB | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
A'' : Subalgebra R S := A ⊔ A'
hA_le : A ≤ A ⊔ A' := le_sup_left
hA'_le : A' ≤ A ⊔ A' ... | case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
A'' : Subalgebra R S := A ⊔ A'
hA_le : A ≤ A ⊔ A' := le_sup_left
hA'_le : A... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
A'' : Subalgebra R S := A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq' | [299, 1] | [320, 10] | simp only [← LinearMap.rTensor_comp, ← LinearMap.comp_apply] at h | case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
A'' : Subalgebra R S := A ⊔ A'
hA_le : A ≤ A ⊔ A' := le_sup_left
hA'_le : A... | case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
A'' : Subalgebra R S := A ⊔ A'
hA_le : A ≤ A ⊔ A' := le_sup_left
hA'_le : A... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
A'' : Subalgeb... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq' | [299, 1] | [320, 10] | exact h | case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
A'' : Subalgebra R S := A ⊔ A'
hA_le : A ≤ A ⊔ A' := le_sup_left
hA'_le : A... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
A'' : Subalgeb... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq' | [299, 1] | [320, 10] | ext | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toLinearMa... | case H
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toL... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq' | [299, 1] | [320, 10] | rfl | case H
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toL... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case H
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTe... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq' | [299, 1] | [320, 10] | ext | R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toLinearMa... | case H
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toL... | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/DirectLimit.lean | TensorProduct.Algebra.eq_of_fg_of_subtype_eq' | [299, 1] | [320, 10] | rfl | case H
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A'.val.toL... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case H
R : Type u_1
S : Type u_2
N : Type u_3
inst✝⁴ : CommRing R
inst✝³ : CommRing S
inst✝² : Algebra R S
inst✝¹ : AddCommGroup N
inst✝ : Module R N
A : Subalgebra R S
hA : A.FG
t : ↥A ⊗[R] N
A' : Subalgebra R S
hA' : A'.FG
t' : ↥A' ⊗[R] N
h : (LinearMap.rTe... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.map | [74, 1] | [80, 38] | unfold IsTopologicallyNilpotent at ha ⊢ | σ : Type u_1
inst✝¹⁰ : DecidableEq σ
R : Type u_2
inst✝⁹ : CommRing R
inst✝⁸ : TopologicalSpace R
inst✝⁷ : TopologicalRing R
S : Type u_3
inst✝⁶ : CommRing S
inst✝⁵ : TopologicalSpace S
inst✝⁴ : TopologicalRing S
φ✝ : R →+* S
hφ✝ : Continuous ⇑φ✝
α : Type u_4
β : Type u_5
inst✝³ : CommRing α
inst✝² : CommRing β
inst✝¹ ... | σ : Type u_1
inst✝¹⁰ : DecidableEq σ
R : Type u_2
inst✝⁹ : CommRing R
inst✝⁸ : TopologicalSpace R
inst✝⁷ : TopologicalRing R
S : Type u_3
inst✝⁶ : CommRing S
inst✝⁵ : TopologicalSpace S
inst✝⁴ : TopologicalRing S
φ✝ : R →+* S
hφ✝ : Continuous ⇑φ✝
α : Type u_4
β : Type u_5
inst✝³ : CommRing α
inst✝² : CommRing β
inst✝¹ ... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝¹⁰ : DecidableEq σ
R : Type u_2
inst✝⁹ : CommRing R
inst✝⁸ : TopologicalSpace R
inst✝⁷ : TopologicalRing R
S : Type u_3
inst✝⁶ : CommRing S
inst✝⁵ : TopologicalSpace S
inst✝⁴ : TopologicalRing S
φ✝ : R →+* S
hφ✝ : Continuous ⇑φ✝
α : Type u_4... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.map | [74, 1] | [80, 38] | simp_rw [← map_pow] | σ : Type u_1
inst✝¹⁰ : DecidableEq σ
R : Type u_2
inst✝⁹ : CommRing R
inst✝⁸ : TopologicalSpace R
inst✝⁷ : TopologicalRing R
S : Type u_3
inst✝⁶ : CommRing S
inst✝⁵ : TopologicalSpace S
inst✝⁴ : TopologicalRing S
φ✝ : R →+* S
hφ✝ : Continuous ⇑φ✝
α : Type u_4
β : Type u_5
inst✝³ : CommRing α
inst✝² : CommRing β
inst✝¹ ... | σ : Type u_1
inst✝¹⁰ : DecidableEq σ
R : Type u_2
inst✝⁹ : CommRing R
inst✝⁸ : TopologicalSpace R
inst✝⁷ : TopologicalRing R
S : Type u_3
inst✝⁶ : CommRing S
inst✝⁵ : TopologicalSpace S
inst✝⁴ : TopologicalRing S
φ✝ : R →+* S
hφ✝ : Continuous ⇑φ✝
α : Type u_4
β : Type u_5
inst✝³ : CommRing α
inst✝² : CommRing β
inst✝¹ ... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝¹⁰ : DecidableEq σ
R : Type u_2
inst✝⁹ : CommRing R
inst✝⁸ : TopologicalSpace R
inst✝⁷ : TopologicalRing R
S : Type u_3
inst✝⁶ : CommRing S
inst✝⁵ : TopologicalSpace S
inst✝⁴ : TopologicalRing S
φ✝ : R →+* S
hφ✝ : Continuous ⇑φ✝
α : Type u_4... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.map | [74, 1] | [80, 38] | apply Filter.Tendsto.comp _ ha | σ : Type u_1
inst✝¹⁰ : DecidableEq σ
R : Type u_2
inst✝⁹ : CommRing R
inst✝⁸ : TopologicalSpace R
inst✝⁷ : TopologicalRing R
S : Type u_3
inst✝⁶ : CommRing S
inst✝⁵ : TopologicalSpace S
inst✝⁴ : TopologicalRing S
φ✝ : R →+* S
hφ✝ : Continuous ⇑φ✝
α : Type u_4
β : Type u_5
inst✝³ : CommRing α
inst✝² : CommRing β
inst✝¹ ... | σ : Type u_1
inst✝¹⁰ : DecidableEq σ
R : Type u_2
inst✝⁹ : CommRing R
inst✝⁸ : TopologicalSpace R
inst✝⁷ : TopologicalRing R
S : Type u_3
inst✝⁶ : CommRing S
inst✝⁵ : TopologicalSpace S
inst✝⁴ : TopologicalRing S
φ✝ : R →+* S
hφ✝ : Continuous ⇑φ✝
α : Type u_4
β : Type u_5
inst✝³ : CommRing α
inst✝² : CommRing β
inst✝¹ ... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝¹⁰ : DecidableEq σ
R : Type u_2
inst✝⁹ : CommRing R
inst✝⁸ : TopologicalSpace R
inst✝⁷ : TopologicalRing R
S : Type u_3
inst✝⁶ : CommRing S
inst✝⁵ : TopologicalSpace S
inst✝⁴ : TopologicalRing S
φ✝ : R →+* S
hφ✝ : Continuous ⇑φ✝
α : Type u_4... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.map | [74, 1] | [80, 38] | convert hφ.tendsto 0 | σ : Type u_1
inst✝¹⁰ : DecidableEq σ
R : Type u_2
inst✝⁹ : CommRing R
inst✝⁸ : TopologicalSpace R
inst✝⁷ : TopologicalRing R
S : Type u_3
inst✝⁶ : CommRing S
inst✝⁵ : TopologicalSpace S
inst✝⁴ : TopologicalRing S
φ✝ : R →+* S
hφ✝ : Continuous ⇑φ✝
α : Type u_4
β : Type u_5
inst✝³ : CommRing α
inst✝² : CommRing β
inst✝¹ ... | case h.e'_5.h.e'_3
σ : Type u_1
inst✝¹⁰ : DecidableEq σ
R : Type u_2
inst✝⁹ : CommRing R
inst✝⁸ : TopologicalSpace R
inst✝⁷ : TopologicalRing R
S : Type u_3
inst✝⁶ : CommRing S
inst✝⁵ : TopologicalSpace S
inst✝⁴ : TopologicalRing S
φ✝ : R →+* S
hφ✝ : Continuous ⇑φ✝
α : Type u_4
β : Type u_5
inst✝³ : CommRing α
inst✝² :... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝¹⁰ : DecidableEq σ
R : Type u_2
inst✝⁹ : CommRing R
inst✝⁸ : TopologicalSpace R
inst✝⁷ : TopologicalRing R
S : Type u_3
inst✝⁶ : CommRing S
inst✝⁵ : TopologicalSpace S
inst✝⁴ : TopologicalRing S
φ✝ : R →+* S
hφ✝ : Continuous ⇑φ✝
α : Type u_4... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.map | [74, 1] | [80, 38] | rw [map_zero] | case h.e'_5.h.e'_3
σ : Type u_1
inst✝¹⁰ : DecidableEq σ
R : Type u_2
inst✝⁹ : CommRing R
inst✝⁸ : TopologicalSpace R
inst✝⁷ : TopologicalRing R
S : Type u_3
inst✝⁶ : CommRing S
inst✝⁵ : TopologicalSpace S
inst✝⁴ : TopologicalRing S
φ✝ : R →+* S
hφ✝ : Continuous ⇑φ✝
α : Type u_4
β : Type u_5
inst✝³ : CommRing α
inst✝² :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_5.h.e'_3
σ : Type u_1
inst✝¹⁰ : DecidableEq σ
R : Type u_2
inst✝⁹ : CommRing R
inst✝⁸ : TopologicalSpace R
inst✝⁷ : TopologicalRing R
S : Type u_3
inst✝⁶ : CommRing S
inst✝⁵ : TopologicalSpace S
inst✝⁴ : TopologicalRing S
φ✝ : R →+* S
hφ✝ : Continuo... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.mul_right | [82, 1] | [94, 36] | intro v hv | σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : LinearTo... | σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : LinearTo... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
ins... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.mul_right | [82, 1] | [94, 36] | rw [LinearTopology.mem_nhds_zero_iff] at hv | σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : LinearTo... | σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : LinearTo... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
ins... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.mul_right | [82, 1] | [94, 36] | rcases hv with ⟨I, _, I_mem_nhds, I_subset⟩ | σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : LinearTo... | case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalS... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
ins... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.mul_right | [82, 1] | [94, 36] | specialize ha I_mem_nhds | case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalS... | case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalS... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continu... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.mul_right | [82, 1] | [94, 36] | simp only [Filter.mem_map, Filter.mem_atTop_sets, ge_iff_le, Set.mem_preimage, SetLike.mem_coe] at ha ⊢ | case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalS... | case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalS... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continu... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.mul_right | [82, 1] | [94, 36] | rcases ha with ⟨n, ha⟩ | case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalS... | case intro.intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : Topolo... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continu... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.mul_right | [82, 1] | [94, 36] | use n | case intro.intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : Topolo... | case h
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : L... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : C... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.mul_right | [82, 1] | [94, 36] | intro m hm | case h
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : L... | case h
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : L... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.mul_right | [82, 1] | [94, 36] | rw [mul_pow] | case h
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : L... | case h
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : L... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.mul_right | [82, 1] | [94, 36] | apply I_subset | case h
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : L... | case h.a
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ :... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.mul_right | [82, 1] | [94, 36] | apply I.mul_mem_right _ (ha m hm) | case h.a
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Typ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.mul_left | [96, 2] | [98, 38] | rw [mul_comm] | σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : LinearTo... | σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : LinearTo... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
ins... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.mul_left | [96, 2] | [98, 38] | exact mul_right hb a | σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : LinearTo... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
ins... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.add | [100, 1] | [117, 43] | intro v hv | σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : LinearTo... | σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : LinearTo... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
ins... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.add | [100, 1] | [117, 43] | rw [LinearTopology.mem_nhds_zero_iff] at hv | σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : LinearTo... | σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : LinearTo... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
ins... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.add | [100, 1] | [117, 43] | rcases hv with ⟨I, _, I_mem_nhds, I_subset⟩ | σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : LinearTo... | case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalS... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
ins... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.add | [100, 1] | [117, 43] | specialize ha I_mem_nhds | case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalS... | case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalS... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continu... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.add | [100, 1] | [117, 43] | specialize hb I_mem_nhds | case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalS... | case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalS... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continu... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.add | [100, 1] | [117, 43] | simp only [Filter.mem_map, Filter.mem_atTop_sets, ge_iff_le,
Set.mem_preimage, SetLike.mem_coe] at ha hb | case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalS... | case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalS... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continu... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.add | [100, 1] | [117, 43] | rcases ha with ⟨na, ha⟩ | case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalS... | case intro.intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : Topolo... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continu... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.add | [100, 1] | [117, 43] | rcases hb with ⟨nb, hb⟩ | case intro.intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : Topolo... | case intro.intro.intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : C... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.add | [100, 1] | [117, 43] | simp only [Filter.mem_map, Filter.mem_atTop_sets, ge_iff_le, Set.mem_preimage] | case intro.intro.intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : ... | case intro.intro.intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.add | [100, 1] | [117, 43] | use na + nb | case intro.intro.intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : ... | case h
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : L... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.add | [100, 1] | [117, 43] | intro m hm | case h
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : L... | case h
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : L... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.add | [100, 1] | [117, 43] | apply I_subset | case h
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ : L... | case h.a
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ :... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.add | [100, 1] | [117, 43] | apply I.add_pow_mem_of_pow_mem_of_le (ha na le_rfl) (hb nb le_rfl) | case h.a
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ :... | case h.a
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ :... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Typ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.add | [100, 1] | [117, 43] | apply le_trans hm (Nat.le_add_right _ _) | case h.a
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝² : CommRing α
inst✝¹ : TopologicalSpace α
inst✝ :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a
σ : Type u_1
inst✝⁹ : DecidableEq σ
R : Type u_2
inst✝⁸ : CommRing R
inst✝⁷ : TopologicalSpace R
inst✝⁶ : TopologicalRing R
S : Type u_3
inst✝⁵ : CommRing S
inst✝⁴ : TopologicalSpace S
inst✝³ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Typ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.IsTopologicallyNilpotent.zero | [119, 1] | [121, 68] | rw [zero_pow (Nat.ne_zero_iff_zero_lt.mpr hi)] | σ : Type u_1
inst✝⁸ : DecidableEq σ
R : Type u_2
inst✝⁷ : CommRing R
inst✝⁶ : TopologicalSpace R
inst✝⁵ : TopologicalRing R
S : Type u_3
inst✝⁴ : CommRing S
inst✝³ : TopologicalSpace S
inst✝² : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
inst✝¹ : CommRing α
inst✝ : TopologicalSpace α
x✝ : ℕ
hi : x✝ ≥ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
R : Type u_2
inst✝⁷ : CommRing R
inst✝⁶ : TopologicalSpace R
inst✝⁵ : TopologicalRing R
S : Type u_3
inst✝⁴ : CommRing S
inst✝³ : TopologicalSpace S
inst✝² : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
α : Type u_4
ins... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.EvalDomain.map | [151, 1] | [157, 26] | apply Filter.Tendsto.comp | σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
a : σ → R
ha : EvalDomain a
⊢ Filter.Tendsto (fun s => φ (a s)) Filter.cofinit... | case hg
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
a : σ → R
ha : EvalDomain a
⊢ Filter.Tendsto ⇑φ ?y (nhds 0)
case hf
σ... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
a : σ → R
ha : Ev... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.EvalDomain.map | [151, 1] | [157, 26] | convert hφ.tendsto 0 | case hg
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
a : σ → R
ha : EvalDomain a
⊢ Filter.Tendsto ⇑φ ?y (nhds 0)
case hf
σ... | case h.e'_5.h.e'_3
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
a : σ → R
ha : EvalDomain a
⊢ 0 = φ 0
case hf
σ : Type u_1... | Please generate a tactic in lean4 to solve the state.
STATE:
case hg
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
a : σ → R... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.EvalDomain.map | [151, 1] | [157, 26] | rw [RingHom.map_zero] | case h.e'_5.h.e'_3
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
a : σ → R
ha : EvalDomain a
⊢ 0 = φ 0
case hf
σ : Type u_1... | case hf
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
a : σ → R
ha : EvalDomain a
⊢ Filter.Tendsto (fun s => a s) Filter.cof... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_5.h.e'_3
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.EvalDomain.map | [151, 1] | [157, 26] | exact ha.tendsto_zero | case hf
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
a : σ → R
ha : EvalDomain a
⊢ Filter.Tendsto (fun s => a s) Filter.cof... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hf
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
a : σ → R... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.Continuous.on_scalars | [181, 1] | [185, 54] | simp only [RingHom.coe_comp] | σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
ε : MvPowerSeries σ R →+* S
hε : Continuous ⇑ε
⊢ Continuous ⇑(ε.comp (C σ R)) | σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
ε : MvPowerSeries σ R →+* S
hε : Continuous ⇑ε
⊢ Continuous (⇑ε ∘ ⇑(C σ R)) | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
ε : MvPowerSeries... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPowerSeries.Continuous.on_scalars | [181, 1] | [185, 54] | exact Continuous.comp hε MvPowerSeries.continuous_C | σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
ε : MvPowerSeries σ R →+* S
hε : Continuous ⇑ε
⊢ Continuous (⇑ε ∘ ⇑(C σ R)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
ε : MvPowerSeries... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPolynomial.coeToMvPowerSeries_denseRange | [188, 1] | [205, 84] | rw [mem_closure_iff_nhds, nhds_pi] | σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
⊢ f ∈ closure (Set.range ⇑coeToMvPowerSeries.ringHom) | σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
⊢ ∀ t ∈ Filter.pi fun i => nhds (f i), (t ∩ Set.range ⇑c... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPolynomial.coeToMvPowerSeries_denseRange | [188, 1] | [205, 84] | intro t | σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
⊢ ∀ t ∈ Filter.pi fun i => nhds (f i), (t ∩ Set.range ⇑c... | σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
t : Set (MvPowerSeries σ R)
⊢ (t ∈ Filter.pi fun i => nh... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPolynomial.coeToMvPowerSeries_denseRange | [188, 1] | [205, 84] | rw [Filter.mem_pi] | σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
t : Set (MvPowerSeries σ R)
⊢ (t ∈ Filter.pi fun i => nh... | σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
t : Set (MvPowerSeries σ R)
⊢ (∃ I, I.Finite ∧ ∃ t_1, (∀... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPolynomial.coeToMvPowerSeries_denseRange | [188, 1] | [205, 84] | rintro ⟨I, hI, p, hp, hp_le⟩ | σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
t : Set (MvPowerSeries σ R)
⊢ (∃ I, I.Finite ∧ ∃ t_1, (∀... | case intro.intro.intro.intro
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
t : Set (MvPowerSeries σ R)... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPolynomial.coeToMvPowerSeries_denseRange | [188, 1] | [205, 84] | obtain ⟨n, hn⟩ := hI.bddAbove | case intro.intro.intro.intro
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
t : Set (MvPowerSeries σ R)... | case intro.intro.intro.intro.intro
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
t : Set (MvPowerSerie... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Co... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPolynomial.coeToMvPowerSeries_denseRange | [188, 1] | [205, 84] | use f.truncFun' n | case intro.intro.intro.intro.intro
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
t : Set (MvPowerSerie... | case h
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
t : Set (MvPowerSeries σ R)
I : Set (σ →₀ ℕ)
hI :... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
h... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPolynomial.coeToMvPowerSeries_denseRange | [188, 1] | [205, 84] | constructor | case h
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
t : Set (MvPowerSeries σ R)
I : Set (σ →₀ ℕ)
hI :... | case h.left
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
t : Set (MvPowerSeries σ R)
I : Set (σ →₀ ℕ)... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowe... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPolynomial.coeToMvPowerSeries_denseRange | [188, 1] | [205, 84] | apply hp_le | case h.left
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
t : Set (MvPowerSeries σ R)
I : Set (σ →₀ ℕ)... | case h.left.a
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
t : Set (MvPowerSeries σ R)
I : Set (σ →₀ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.left
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : M... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Evaluation.lean | MvPolynomial.coeToMvPowerSeries_denseRange | [188, 1] | [205, 84] | simp only [Set.mem_pi] | case h.left.a
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
t : Set (MvPowerSeries σ R)
I : Set (σ →₀ ... | case h.left.a
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f : MvPowerSeries σ R
t : Set (MvPowerSeries σ R)
I : Set (σ →₀ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.left.a
σ : Type u_1
inst✝⁶ : DecidableEq σ
R : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : TopologicalSpace R
inst✝³ : TopologicalRing R
S : Type u_3
inst✝² : CommRing S
inst✝¹ : TopologicalSpace S
inst✝ : TopologicalRing S
φ : R →+* S
hφ : Continuous ⇑φ
f :... |
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